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Beliefs and attitudes in mathematics teaching and learning Trygve Breiteig, Barbro Grevholm, Kirsti Kislenko Introduction Beliefs play great role in mathematics learning and teaching. The learning outcomes of students are strongly related to their beliefs and attitudes about mathematics (Furinghetti & Pehkonen, 2000). Thus assessing or evaluating of students’ mathematical knowledge must be made in awareness of their beliefs. During the last twenty years the research area about beliefs and attitudes has grown considerably, and many different countries have been included in the research - the work of Erkki Pehkonen who has made several investigations in Finland; Peter Kloosterman from United States of America, Günter Törner from Germany, Gilah C. Leder from Australia, and many others. They have been looking for answers to several different questions. For example, Kloosterman asked (2002): “What do students think mathematics is and how does one learn mathematics?”; Pehko...

Cause and effect Definiton and example Temporal sequance identifying changes in topic, and we can signal important words, phrases, and ideas by making them look different from the surrounding text. Let’s examine how we can use headings, layout, and typographical variations to signal the learner. Headings Authors use headings to signal a change of topic and to provide the learner with a picture of how the materials are organized. The use of headings to signal changes of topic is prominent even in electronic documents. The tags used to create web pages for the Internet provide six different levels of headings for a web document (see examples of two of these heading levels in Figure 8-1). Headings are key words or short phrases that identify the content of the sections of text information. Headings can emphasize either a sequential organization of topics or a hierarchical organization (Lorch et al., 2011a). Headings that communicate a hierarchical organizat...

Expert’sEdge The 10% Solution (for Learning) One of the most widely disseminated nostrums in education and training is the ‘‘retention chart,’’ which typically is phrased, ‘‘People generally remember 10% of what they read, 20% of what they hear, 30% of what they see, 50% of what they hear and see, 70% of what they say or write, 90% of what they say as they do a thing.’’ Where does this nostrum come from? You will see it attributed to Edgar Dale, Jerome Bruner, William Glasser, and many other sources. All these attributions are entirely bogus. The most likely author is Paul John Phillips, who prepared training materials for the petroleum industry at the University of Texas in the summers of 1939 and 1940. Phillips then spent the World War II years as a lieutenant colonel in charge of the Training Methods branch oftheOrdnanceSchool,Aberdeen Proving Ground. After the war he return ed to the University of Texas. Records at the University of Texas show that Phillips developed a mimeographe...

MESSAGE DESIGN FOR TEXT An instructional unit—whether a textbook, printed manual, computer-based instruction, multimedia instruction, or video recording—is an artifact of the design process that will endure (Simon, 1981). This artifact represents the interface or interaction between the learner and the instructional materials. In Simon’s terms, the artifact will serve its purpose if it is appropriate for the learner. Thus, our task as designers is to create an appropriate interface between the instructional materials and the learner. One part of this process is to design the message so that it is communicated effectively. In this section, we consider how we can design the message by manipulating the text (e.g., structure of the writing) and the typography. After analyzing science textbooks, Chambliss and Calfee (1989) concluded that there are three critical design elements essential to good printed instruction. First is a set of distinctive elements such as words or typography that ...